Direct-conversion architecture-based orthogonal frequency division multiplexing (OFDM) systems are troubled by impairments such as in-phase and quadrature-phase (I/Q) imbalance and carrier frequency offset (CFO). These impairments are unavoidable in any practical implementation and severely degrade the obtainable link performance. In this contribution, we study the joint impact of frequency-selective I/Q imbalance at both transmitter and receiver together with channel distortions and CFO error. Two estimation and compensation structures based on different pilot patterns are proposed for coping with such impairments. The first structure is based on preamble pilot pattern while the second one assumes a sparse pilot pattern. The proposed estimation/compensation structures are able to separate the individual impairments, which are then compensated in the reverse order of their appearance at the receiver. We present time-domain estimation and compensation algorithms for receiver I/Q imbalance and CFO and propose low-complexity algorithms for the compensation of channel distortions and transmitter IQ imbalance. The performance of the compensation algorithms is investigated with computer simulations as well as with practical radio frequency (RF) measurements. The performance results indicate that the proposed techniques provide close to the ideal performance both in simulations and measurements.

With the ever-increasing demand for high data rates and high quality of services for end users, bandwidth-efficient transmission schemes such as orthogonal frequency division multiplexing (OFDM) are being adopted in emerging wireless communication systems (e.g., WLAN 802.11a/g/n [

The frequency up- and downconversion in the direct-conversion architectures are implemented by I/Q mixing, which suffers from the amplitude and phase mismatch between the I- and Q- branches [

CFO is another important RF impairment, particularly associated with OFDM-based communication systems. It is caused by the instability of local oscillator and also due to the mobility of users [

In this paper, we consider DSP-based compensation of frequency-selective transmitter and receiver I/Q imbalance together with frequency-selective channel and CFO in the OFDM system context. The central theme is to first systematically formulate the baseband equivalent of the received signal. Based on this signal model, we propose new low-complexity decoupled estimation and compensation algorithms. Unlike the joint estimation algorithms (e.g., [

The novelty of this paper is as follows:

We do not make any specific assumption about the location of pilots for sparse pilot-based estimation and compensation structure. The existing algorithms, for example [

In this work, instead of proposing comprehensive and brand new algorithms to cope with multiple RF impairments at once, we simplify the complexity of the problem by reforming overall receiver design and decoupling the effects of individual RF impairments. Then incorporating already existing efficient algorithms with new proposed methods, a hybrid time-and-frequency domain compensation architecture with very reasonable complexity and good performance is achieved.

Practical RF measurements are used to verify the applicability of algorithms in real-world receiver design which, to the best of authors’ knowledge, has not been addressed so far in the literature. The performance of individual impairments has been evaluated though, for example, [

Here we use two widely deployed pilot patterns in the current and upcoming OFDM-based radio systems (e.g., IEEE 802.11n [

An attractive feature of receiver I/Q imbalance compensation algorithm is that it is able to track the time-variation of I/Q imbalance and updates the coefficients of compensation filter appropriately.

The paper is organized as follows. I/Q imbalance model and its impact, OFDM signal model under frequency-selective I/Q imbalances, channel distortions, and CFO are described in Section

The direct-conversion transmitter architecture is based on the principle of directly I/Q upconverting the baseband signal to the RF frequency. The upconversion is performed in the analog domain by a quadrature mixer, which theoretically provides infinite image signal attenuation. This eliminates the need for image rejection filter, relaxing the overall requirement for RF filtering. A perfectly balanced modulator corresponds to equal gain and

Block diagram of Frequency-selective transmitter I/Q imbalance model.

On the receiver side, the RF signal is downconverted to baseband using a quadrature demodulator. The downconverted baseband equivalent of the received signal

The

We consider an OFDM system with

Referring to Figure

OFDM system model with I/Q imbalance and CFO.

Assume now that the local oscillator of transmitter and receiver are not synchronized and a CFO

In this paper, we assume that the length of the cascade of impulse responses of the transmitter I/Q imbalance filters (

The estimation and compensation of radio frequency impairments in OFDM systems can be performed blindly and/or with the aid of training (a.k.a. pilot) symbols. For forming such pilot-symbol-assisted OFDM systems, it involves inserting the known symbols in the stream of data symbols. With practical system design, two types of pilot patterns are widely used—the preamble pilot pattern that amends an entirely known OFDM symbol at the beginning of the frame and the sparse pilot pattern where pilot symbols are sparsely inserted at some subcarriers of specific OFDM symbols. Figure

Pilot structure (a) preamble (b) scattered.

In the following, we discuss receiver-based estimation and compensation algorithms for mitigating all the considered RF impairments. With developed signal model and given pilot patterns, we are able to isolate them individually and then process them for estimation and compensation in the reverse order of their appearance in the transmitter and receiver front end. We first discuss the receiver I/Q imbalance estimation and compensation, which is performed in time domain and is independent of the pilot pattern. Then, two low-complexity and novel structures are proposed for CFO, channel, and transmitter I/Q imbalance compensation with both preamble and sparse pilot structures. The CFO estimation and compensation is also carried out in time domain, while the channel and transmitter IQ imbalance are compensated in frequency domain.

For receiver I/Q imbalance estimation and compensation, we propose to utilize the statistical signal processing-based blind I/Q imbalance compensation algorithms, developed in authors’ earlier work [

For notational simplicity, we drop the noise term in (

Applying the optimum compensation filter to (

The compensation structure proposed in this section utilizes one complete pilot OFDM symbol embedded in the OFDM frame. The preamble pilot symbol is transmitted at the beginning of the transmission to estimate the RF impairments. This kind of pilot pattern assumes that the channel remains static over several OFDM symbols and has the benefit of efficiently using the available bandwidth. OFDM-based systems such as IEEE 802.11 n and IEEE 802.16d have a preamble at the beginning of the frame [

OFDM system model with preamble pilot compensator structure.

There exists an abundant literature on CFO estimation (see, e.g, [

Assuming perfect CFO estimate is obtained, we perform CFO compensation in time domain by multiplying the time domain equivalent of (

The joint transmitter I/Q imbalance and channel equalization are carried out in frequency domain. To simplify the analysis further, let us define the direct and image signal filters as

With ZF equalization scheme, the estimate of original transmit symbols is obtained by solving (

Alternatively, the transmitted symbols can be estimated using ML detection principle which is based on the principle of minimizing the cost function

We consider the LS estimation of the joint transmitter I/Q imbalance and channel filters

We switch to matrix-vector algebra and write the time-domain received symbol corresponding to preamble pilot as

OFDM systems such as LTE and DVB-T/H do not include a preamble pilot in their frame, rather the pilot tones are inserted sparsely in the OFDM symbols. DVB-T/H standard defines both continual and scattered pilots, on the other hand, LTE includes pilot subcarriers only on specified OFDM symbols. Figure

LTE reference pilot structure.

One big challenge with sparse located pilot structure is that the pilots are most likely not allocated to mirror-frequency pairs which is required by most of the pilot-based algorithms developed in literature, for example, [

OFDM system model with sparse pilot compensator structure.

For the CFO estimation, we again apply the two-step time-domain approach of [

With the sparse pilot structure, we propose to compensate the channel and transmitter I/Q imbalance successively. Algorithm

Estimate widely-linear filter

Switch to subcarrier model and write (

Divide (

Hard-decision-based detection of the mirror subcarriers of equalized symbol, given by

At the pilot subcarriers, we now have

From above equation, we find the compensation filter at the pilot subcarriers as

Interpolate

The estimated symbols are then given as

The filter

Here, we derive the transformation for the interpolation of filter

In practice, some of the coefficients of

In Table

Computational complexities per OFDM symbol for different compensation stages.

Algorithms | Complex multiplications |
---|---|

Rx. I/Q imbalance compensation | |

CFO compensation | |

Channel equalization | |

Tx. I/Q imbalance compensation |

The overall complexity of the proposed compensation schemes is

Conceptually, a conventional channel equalizer in the absence of CFO and I/Q imbalances operates on a per-subcarrier basis, requiring 1 complex multiplication per active subcarrier. However, a joint equalizer for channel, CFO, and Tx. Rx. imbalances has to take into account the contribution of all active subcarriers. Therefore, for such an equalizer with

The performance of proposed algorithms is illustrated in this section with computer simulations. We first evaluate the performance of CFO estimator in the presence of transmitter I/Q imbalance and channel distortions and do not take into account receiver I/Q imbalance, for both preamble and sparse pilot structures. Then, SER simulations are performed to evaluate the detection performance of compensation schemes in the presence of transmitter and receiver I/Q imbalance, channel distortions, and CFO.

The parameters considered for CFO estimator simulations are as follows: OFDM-based system with 64-QAM subcarrier modulation, total number of subcarriers

Figures

MSE of preamble pilot-based CFO estimator versus normalized CFO for 64-QAM OFDM syste; 39-tap veh. A channel model; ensemble average of 500 independent channel realizations.

MSE of sparse pilot-based CFO estimator versus normalized CFO for 64-QAM OFDM syste; 39-tap veh. A channel model; ensemble average of 500 independent channel realizations.

Now, we perform the SER simulations and illustrate the results by plotting the mean SER as a function of received SNR. A typical 64-QAM OFDM system is considered whose parameters are given in Table

System parameters.

Total number of subcarriers | |

Active subcarriers | |

Cyclic prefix length | |

Subcarrier spacing | |

Sampling Frequency | |

Channel type | vehicular A |

No. of channel taps | 39 |

Gain imbalance | |

Phase imbalance | |

I-branch filter | |

Q-branch filter |

In the following figures, legend “No FE Distortion” refers to the case when no transmitter and receiver I/Q imbalance and CFO is present and known channel estimates are used for channel equalization, “W/o Compensation” refers to when all radio impairments are present and only channel is equalized with known estimates, and “W/Tx Rx IQ Imbalance only” for the case when only transmitter and receiver IQ imbalance is present and channel is equalized with known estimates. “W/ZF Compensation” “W/ML Compensation” “W/LS Compensation”, and “W/WLS Compensation” legends exemplify the schemes proposed in Section

For preamble pilot-based compensation, we transmit 50 OFDM symbols and use first OFDM symbol as pilot. In each simulation run, we generate a random CFO in the range

Preamble pilot-based SER versus SNR performance curves for 64-QAM OFDM system. Tx/Rx FE IRR = 20–30 dB; veh. A channel model with 39 taps; ensemble average over 1000 independent channel realizations.

The OFDM signal model for sparse pilot-based compensation is similar to LTE frame structure shown in Figure

Sparse pilot-based SER versus SNR performance curves for 64-QAM OFDM system. Tx/Rx FE IRR = 20–30 dB; veh. A channel model with 39 taps; ensemble average over 1000 independent channel realizations.

In order to further validate the performance of proposed compensation algorithms, real-world RF measurements have been performed. We first summarize the overall measurement setup and then describe the measurement procedure in detail.

The generic structure of the measurement setup is identical to the one shown in Figures

General structure of the measurement setup consisting of laboratory instruments and I/Q modulator and demodulator.

A computer with MATLAB is used for performing digital signal processing-related tasks and also for instrument control. The baseband OFDM signal with parameters similar to simulations as in Section

We first shortly address the estimation of front-end IRR of AD8349 and MAX2023 chips, without any compensation. Although the exact values of gain and phase imbalance of these chips are unknown, the IRR analysis is still possible using LS fitting approach as follows. We denote the reference time domain signal

In Figure

Comparison of averaged FE IRR versus frequency for different imbalance filter lengths. LO frequency = 1.5 GHz.

The performance of blind receiver I/Q imbalance compensation algorithm is evaluated next. Here, R&S SMJ acts as transmitter to produce RF signal (with no transmitter IQ imbalance and channel distortions) and MAX2023 to demodulate the signal. The digitized baseband signal (with receiver I/Q imbalance) is transferred to computer through GPIB, where we apply blind DSP algorithm for compensation. The data captured from oscilloscope, however, cannot be used directly for compensation but rather it is first processed to remove the RF chain errors. That involves resampling, delay removal, phase synchronization, offset cancellation, and scaling. After these steps, we apply the compensation algorithm. For illustration purpose, we use a half-loaded OFDM signal with 300 active subcarriers (out of total 1024). The LO frequency is 1.5 GHz. Figure

Comparison of measured I/Q demodulator output before and after I/Q imbalance compensation.

The performance analysis of pilot-based compensation schemes is carried out by creating an OFDM waveform with parameters given in Table

The example waveform used for preamble pilot-based compensation algorithms is an OFDM signal with same parameters as were in simulations. In the measurements, we transmit 10 OFDM symbols and use one known OFDM symbol during the estimation and calibration phase. The CFO is 10 KHz and a 3-tap compensation filter for receiver I/Q imbalance compensation and also for transmitter I/Q imbalance estimation. Both ML and ZF equalization schemes are applied to the signal, after receiver I/Q imbalance and CFO compensation. With a fixed channel, the obtained results ensemble averaged over 10 independent measurements are plotted. Figure

Preamble pilot-based measured MSE of CFO versus SNR performance curve. CFO = 10 KHz.

Measured SER versus SNR performance curves for 64-QAM OFDM system with preamble pilot; CFO = 10 KHz; veh. A channel model with 39 taps; ensemble average over 10 realizations with a fixed channel.

Measured constellation diagram of 64-QAM OFDM system before and after RF impairments mitigation. (a) Uncompensated (b) Compensated with ZF equalization.

In the second measurement example, the signal is an OFDM signal having 10 symbols and pilots located at every sixth subcarrier. The signal has altogether 600 active subcarriers out of 1024 subcarriers, with 15 KHz subcarrier spacing. Therefore, in total, there are 1000 pilot symbols. The signal is oversampled by 2. The CFO is now 45 KHz that is greater than the subcarrier spacing. Again the receiver I/Q imbalance is compensated with 3-taps, and the LS and WLS approaches discussed in Section

Sparse pilot-based measured MSE of CFO versus SNR performance curve.

Measured SER versus SNR performance curves for 64-QAM OFDM system with sparse pilot;

Measured constellation diagram of 64-QAM OFDM system with RF impairments mitigation. (a) Compensated with LS method (b) Compensated with WLS method.

In general, it can be concluded from the measurements results of Figures

In practice, the measurement setup is exposed to variety of errors, which must be corrected before introducing channel distortion and noise as well as before applying the compensation algorithms. We briefly review these errors now.

The downconversion of RF signal (with transmitter I/Q imbalance) using R&S

Similar to R&S FSG, the data captured from oscilloscope must be DSP conditioned before being used in actual estimation and compensation. The data conditioning involves resampling to original signal sample rate, delay estimation, and offset removal with already-mentioned algorithms.

In this paper, the performance of OFDM-based communication systems is studied in the presence of frequency-selective I/Q imbalance, channel distortions and CFO. Based on our signal model, generally applicable algorithms have been developed for the compensation of such impairments. The proposed methods are composed of time domain and frequency domain compensation. It is shown with simulations that the proposed, estimator and compensator structures produce symbol error rates close to the ideal ones. A laboratory measurement setup is also proposed and extensive measurements are carried out to prove the practical value of the algorithms. The measurements results show that the achievable SER is close to the ideal. Hence, the compensation algorithms provide significant improvement to obtainable link performance and can be used in real world radio transceivers. Future work will focus on generalizing the work to MIMO-OFDM and a real-time prototype implementation using FPGA’s for the digital parts and integrated RF-ASIC’s for the analog circuitry.

This work was supported by the Technology Promotion Foundation of Finland (TES), the Nokia Foundation, the graduate school TISE, the Austrian Center of Competence in Mechatronics (ACCM), the Academy of Finland (under the projects “Digitally-Enhanced RF for Cognitive Radio Devices” and “Joint Analysis and DSP-Based Mitigation of Multiple RF Impairments in Future Radio Devices”), and the Finnish Funding Agency for Technology and Innovation (Tekes; under the project “Enabling Methods for Dynamic Spectrum Access and Cognitive Radio”), all of which are gratefully acknowledged. The authors would also like to thank the anonymous reviewers for their helpful comments and suggestions.